Sharpening and smoothing is fundamental to image enhancement and restoration. Image enhancement refers to accentuation of features of an image such as edges, boundaries, or contrast, and includes noise reduction, edge crisping and sharpening, filtering and many often well-known processes. Image restoration usually involves filtering an observed image to minimize, as best as possible, the effort of degradation. See A. K. Jain Fundamentals of Digital Image Processing, and W. Pratt, Digital Image Processing. Sharpening and smoothing are commonly used techniques in digital photography and scientific and medical imaging.
A popular sharpening method is referred to as unsharp masking which filters the image with a special highpass filter. A disadvantage of unsharp masking is that noise in the image is also sharpened and that the resulting output often looks “unnatural” since the choice of the appropriate degree of sharpening is difficult.
There exist many sharpening filters for image processing. These sharpening filters magnify the edges in an image, typically by highpass-filtering of the original image. A common method is unsharp masking as described in, for example, “Fundamentals of Digital Image Processing,” by A. K. Jain, Prentice Hall, 1989.
In unsharp masking, given an image f(x), a sharpened image fsharp(x) is obtained by adding a magnified gradient image to a smoothed (“unsharped”) version of the image, i.e.fsharp(x):=fsmooth(x)+λfgradient(x)  (1)where λ>1 is the sharpness parameter. The sharpness increases with increasing λ. If the image f(x) can be written as a sum of a lowpass filtered image flow and a highpass filtered image fhigh then Eq.(1) can be expressed asfsharp(x)=flow (x)+(λ−1) fhigh(x).  (2)In this approach the lowpass and highpass filters are fixed. One problem with this approach is that a priori it is not known what filter size, filter coefficients, and what value for the parameter λ is appropriate. If λ is too large, the image looks unnatural. To overcome this problem, some approaches apply several filters and take that output which looks most “natural” (see e.g., “Real World Scanning and Halftones,” Peachpit Press, Inc., Berkeley, 1993 by D. Blatner, S. Roth).
In order to overcome the problem of sharpening not only “real” edges, but also noise pixels, the approach in “Adaptive Unsharp Masking for Contrast Enhancement,” in Proceedings of the 1997 International Conference on Image Processing (ICIP '97), pp. 267–270, 1997, by A. Polesel, G. Rampoui and V. J. Mathews, adds an adaptive directional component to an unsharp masking filter in the pixel domain that changes the sharpening parameter depending on strength and orientation of an edge. The unsharp masking filter is a two-dimensional Laplacian.
As mentioned above, the unsharp masking technique raises the problem of determining the degree of sharpening of an image that is best (i.e., finding the correct amount of sharpening). One solution to this problem is addressed in U.S. Pat. No. 5,867,606, entitled “Apparatus and Method for Determining the Appropriate Amount of Sharpening for an Image,” issued Feb. 2, 1999, assigned to Hewlett-Packard Company, Palo Alto, Calif., for using the Laplacian in the unsharp masking technique. As a solution the magnitude of the sharpening parameter λ is determined by matching the Fourier spectrum of the sharpened image with a spectrum of a low resolution version of the original image. This requires in addition to the unsharp masking filters, a Fourier transform on the original image which has a higher computational complexity than a discrete wavelet transform. Furthermore, only one lower resolution image is incorporated into the technique.
The problem of enhancing a scanned document, such as, sharpening of scanned images in the JPEG domain is discussed in “Text and Image Sharpening of Scanned Images in the JPEG Domain,” Proceedings of the 1997 International Conference on Image Processing (ICIP '97), pp. 326–329, 1997 by V. Bhaskaran, K. Konstantinides and G. Beretta. One proposed solution consists of a scaling of the encoding quantization tables to enhance high frequencies. The amount of scaling depends on the energy contained in the corresponding DCT coefficients. Since DCT functions form only a basis in L2 (R), but not in more sophisticated smoothness spaces as, e.g., Hoelder spaces Cα(R), JPEG compression introduces blocky artifacts, a well-known problem in JPEG-compressed images. Those artifacts can be even magnified by scaling the DCT coefficients.
Wavelet coefficients have been modified for the purpose of contrast enhancement in images using criteria such as minimizing the mean-squared-error. However, these approaches do not consider the theoretical smoothness properties of an image in terms of local regularity and are computationally more complex.
In the prior art, detail versions of the image have been processed. Such an approach is described in U.S. Pat. No. 5,805,721, “Method and Apparatus for Contrast Enhancement,” issued Sep. 8, 1998, assigned to Agfa-Gevaert, Belgium. In this approach, the image is decomposed into detail images at different resolutions and a lowpass image. This decomposition is not a subband decomposition, but a Laplacian pyramid where the reconstruction process consists of simply adding detail and lowpass images. The detail coefficients are multiplied with factors that depend on the magnitude of wavelet coefficients. This multiplication can be described by evaluating a monotonic function. This function has power-law behavior, but does not change over scales. In a renormalization step, the pixels in the detail images are first normalized by the possible maximum of the pixels in the detail images. There is no discussion on how to choose the parameter contained in the monotonic function.
Modifications of wavelet coefficients have also been made based on energy criteria. For example, contrast enhancement in images by modifying wavelet coefficients based on energy criteria is described in “De-Noising and Contrast Enhancement Via Wavelet Shrinkage and Nonlinear Adaptive Gain,” Proceedings of the SPIE, Vol. 2762, pp. 566–574, Orlando, Fla., 1996 by X. Zong, A. F. Laine, E. A. Geiser and D. C. Wilson. One problem with this approach is that many computations are required because a comparison of local energy is performed for each individual wavelet coefficient. Furthermore, the modifications only apply to critically sampled wavelet transforms.
Embodiments of the present invention avoid or overcome one or more of the above mentioned problems.